The car traveller
Mr. X, a criminal is escaping by car from the prison at a particular speed. After one hour, the police vehicles start to follow him in a vehicle with a speed 1.5 times that of the car of Mr. X. After how much time (hours) since the escape of Mr. X, will the police catch him? (Assume all other factors to be constant)
The answer is 3.
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The police was behind one hour of Mr X, so we need to account this is the time taken by to catch him. Let v be the speed and t the time in hours.
Escaped distance = pursued distance
( speed of Mr X ) × ( time spent escaping ) = ( speed of police ) × ( time spent pursuing)
v × t = ( 1.5v ) × ( t – 1 )
vt = 1.5vt – 1.5v
1.5v = 1.5vt – vt = 0.5vt
t = 1.5v / 0.5v = 3 hours